Finite Group Databasebeta

← #11897653

Subgroups — #11897653

Order 1152.

740 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5539C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592717C211yesmaximal, characteristic
4C3×#5007C211yesmaximal, characteristic
5#10591410C211yesmaximal, characteristic
6#10591408C211yesmaximal, characteristic
7#10591405C211yesmaximal, characteristic
8#10591401C211yesmaximal, characteristic
9#10590492C211yesmaximal, characteristic, complemented
10#10590488C211yesmaximal, characteristic, complemented
11#10590418C211yesmaximal, characteristic, complemented
12#10590411C211yesmaximal, characteristic, complemented
13#10590315C211yesmaximal, characteristic, complemented
14#10590292C211yesmaximal, characteristic, complemented
15#10590252C211yesmaximal, characteristic, complemented
16#83631—31nomaximal
17#80960—31nomaximal
18C32×C4×D4C2211yescharacteristic
19C2×#3754C2211yescharacteristic
20C4×#634C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×#924—21no—
24C2×C3×Dic3⋊C4—21no—
25C3×#890C2211yescharacteristic
26C3×#888C2211yescharacteristic
27C3×#878—21no—
28C3×#878—21no—
29C3×#870C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32#63919—21no—
33#63918C2211yescharacteristic
34#63918C2211yescharacteristic
35#63844C2211yescharacteristic
36#63844C2211yescharacteristic
37#63843—21no—
38#63839—21no—
39#63839—21no—
40#63659C2211yescharacteristic
41#63637C2211yescharacteristic
42#63634C2211yescharacteristic
43#63630C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#807C2211yescharacteristic
47C3×#807C2211yescharacteristic
48C3×C4⋊(C3⋊C8)C2211yescharacteristic
49#63576C2211yescharacteristic
50#63576C2211yescharacteristic
51#63575C2211yescharacteristic
52#63574C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55Dic3⋊(C3⋊C8)C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#554—31no—
62#5722—31no—
63Q8×Dic6—31no—
64#5539D311yescharacteristic
65C3×#474—31no—
66#5091—31no—
67#5081—31no—
68#5078—31no—
69#5064—31no—
70#5064—31no—
71#5063—31no—
72#5063—31no—
73#5024—31no—
74#5018—31no—
75#5018—31no—
76#5018—31no—
77#5018—61no—
78C4×#214—31no—
79#5008—31no—
80#5007—31no—
81#5007D311yescharacteristic
82#4877—31no—
83#4876—31no—
84#4875—31no—
85#4874—31no—
86#4829—31no—
87#4828—31no—
88#4761—31no—
89#4759—31no—
90#4758—31no—
91#4757—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×#634C2311yescharacteristic
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6—21no—
99C2×C3×Dic6D411yescharacteristic
100C2×#627—21no—
101C2×#627—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C22⋊C4—21no—
104C32×C42C2311yescharacteristic
105#3754Q814yescomplemented
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#217—21no—
112C3×#217—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3D411yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4D411yescharacteristic
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136#3385—91noSylow
137C3×C4⋊Q8—31no—
138C3×C4⋊Q8—31no—
139C3×#125—31no—
140C3×#125—31no—
141C3×C22⋊Q8—61no—
142C3×C22⋊Q8—61no—
143C3×C22⋊Q8—61no—
144C3×C4×Q8—31no—
145C3×C4×D4—21no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148C3×C4×D4C2×D311yescharacteristic
149C3×C4×D4C2×D311yescharacteristic
150C2×C3×C4⋊C4—61no—
151Q8×Dic3—61no—
152#944—61no—
153#944—61no—
154D4×Dic3C2×D311yescharacteristic
155D4×Dic3C2×D311yescharacteristic
156C2×#214—31no—
157C2×#214—31no—
158C2×#214—61no—
159#924—21no—
160C2×Dic3⋊C4—21no—
161#890C2×D311yescharacteristic
162#888—31no—
163#888—31no—
164#888—61no—
165#888—61no—
166#888—61no—
167#888—61no—
168#888C2×D311yescharacteristic
169#887—31no—
170#887—31no—
171#887—61no—
172#878—21no—
173#878—21no—
174#870C2×D311yescharacteristic
175#869—31no—
176#869—31no—
177#869C2×D311yescharacteristic
178C4×Dic6—31no—
179C4×Dic6—31no—
180C4×Dic6—31no—
181C4×Dic6—31no—
182C4×Dic6—61no—
183C4×Dic6C2×D311yescharacteristic
184C3×#107—31no—
185C3×#107—31no—
186C3×C4⋊C8—31no—
187C3×#102—31no—
188C3×#102—31no—
189#832—31no—
190#832—31no—
191#832—61no—
192#832C2×D311yescharacteristic
193#832C2×D311yescharacteristic
194#818—31no—
195#817—31no—
196#816—31no—
197#816—31no—
198#815—31no—
199Dic3⋊C8—31no—
200Dic3⋊C8—31no—
201C8×Dic3—31no—
202#810—31no—
203#810—31no—
204#810—31no—
205#810—31no—
206#810—61no—
207#808—31no—
208#808—31no—
209#808—31no—
210#808—31no—
211#808—31no—
212#807—31no—
213#807—31no—
214#807—31no—
215#807—31no—
216#807—31no—
217#807—31no—
218#807—31no—
219#807—61no—
220#807C2×D311yescharacteristic
221#807C2×D311yescharacteristic
222C4⋊(C3⋊C8)—31no—
223C4⋊(C3⋊C8)—31no—
224C4⋊(C3⋊C8)C2×D311yescharacteristic
225#803—31no—
226#803—31no—
227#803—31no—
228#803—61no—
229C4×C3⋊C8—31no—
230C23×C32—21no—
231C32×D4—21no—
232C32×D4C2×Q812yes—
233C2×C32×C4—21no—
234C2×C32×C4—81no—
235C2×C32×C4C2×D411yescharacteristic
236C2×C32×C4C2×D411yescharacteristic
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240#634—21no—
241#634C2×Q812yes—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—42no—
247C2×C3×Dic3—81no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×Dic6—22no—
253C3×Dic6—81no—
254C3×Dic6—81no—
255#627—81no—
256#627—81no—
257C3⋊(C3⋊C8)—21no—
258C3⋊(C3⋊C8)C2×Q812yes—
259C3×C3⋊C8—21no—
260C3×C3⋊C8—21no—
261Q82—91no—
262#554—31no—
263#501—91no—
264#501—91no—
265#500—91no—
266#479—91no—
267#479—91no—
268#477—91no—
269#476—91no—
270#474—31no—
271#474—91no—
272#446—91no—
273#440—91no—
274#440—91no—
275C4×SD16—91no—
276C2×C3×Q8—31no—
277C2×C3×Q8—61no—
278C2×C3×Q8—61no—
279C2×C3×D4—21no—
280C2×C3×D4C22×D311yescharacteristic
281C2×C3×D4C22×D311yescharacteristic
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—41no—
285C22×C3×C4—61no—
286C22×C3×C4—61no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C2×Dic6—21no—
290C2×Dic6—21no—
291C2×Dic6—31no—
292C2×Dic6—31no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6#6711yescharacteristic
299C2×C3×C8—31no—
300C2×C3×C8—31no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—31no—
303C3×C4⋊C4—31no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C22⋊C4—21no—
318C3×C22⋊C4—21no—
319C3×C22⋊C4—41no—
320C3×C22⋊C4—61no—
321C3×C22⋊C4—61no—
322C3×C42—21no—
323C3×C42—31no—
324C3×C42—31no—
325C3×C42C22×D311yescharacteristic
326C3×C42C22×D311yescharacteristic
327#217—21no—
328#217—21no—
329#214—34no—
330#214—34no—
331#214—64no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3#6711yescharacteristic
340C4⋊Dic3C22×D311yescharacteristic
341C4⋊Dic3C22×D311yescharacteristic
342C4⋊Dic3C22×D311yescharacteristic
343C4⋊Dic3C22×D311yescharacteristic
344Dic3⋊C4—21no—
345Dic3⋊C4—21no—
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348Dic3⋊C4—61no—
349Dic3⋊C4—61no—
350Dic3⋊C4—61no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—121no—
357Dic3⋊C4#6711yescharacteristic
358Dic3⋊C4#6711yescharacteristic
359C4×Dic3—61no—
360C4×Dic3—61no—
361C4×Dic3—61no—
362C4×Dic3—61no—
363C4×Dic3—61no—
364C4×Dic3—61no—
365C4×Dic3—121no—
366C4×Dic3C22×D311yescharacteristic
367C4×Dic3C22×D311yescharacteristic
368C2×C3⋊C8—31no—
369C2×C3⋊C8—31no—
370C2×C3⋊C8—31no—
371C2×C3⋊C8—31no—
372C2×C3⋊C8—61no—
373C2×C3⋊C8—61no—
374C2×C3⋊C8C22×D311yescharacteristic
375C2×C3⋊C8C22×D311yescharacteristic
376C22×C32—22no—
377C22×C32—41no—
378C22×C32—41no—
379C22×C32C22×D411yescharacteristic
380C32×C4—21no—
381C32×C4—21no—
382C32×C4—41no—
383C32×C4C22×Q811yescharacteristic
384C32×C42−1+411yescharacteristic
385C3⋊Dic3—22no—
386C3⋊Dic3—41no—
387C3×Dic3—21no—
388C3×Dic3—21no—
389C3×Dic3—21no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3—41no—
394C3×Dic3#13712yes—
395C2×SD16—91no—
396C4⋊Q8—31no—
397C4⋊Q8—31no—
398C4⋊Q8—91no—
399C4⋊Q8—91no—
400C4⋊Q8—181no—
401C4⋊Q8—181no—
402C4⋊Q8—181no—
403#125—31no—
404#125—31no—
405C22⋊Q8—61no—
406C22⋊Q8—61no—
407C22⋊Q8—61no—
408C4×Q8—31no—
409C4×Q8—91no—
410C4×Q8—91no—
411C4×Q8—91no—
412C4×Q8—181no—
413C4×D4—31no—
414C4×D4—31no—
415C4×D4D3211yescharacteristic
416C2×C4⋊C4—61no—
417#107—31no—
418#107—31no—
419#107—91no—
420#107—91no—
421#107—91no—
422#107—91no—
423#106—91no—
424#106—91no—
425#106—91no—
426C4⋊C8—31no—
427C4⋊C8—91no—
428C4⋊C8—91no—
429#103—91no—
430#103—91no—
431#103—91no—
432#102—31no—
433#102—31no—
434#102—91no—
435#97—91no—
436#97—91no—
437C4×C8—91no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—41no—
441C3×Q8—62no—
442C3×Q8—241no—
443C3×Q8—241no—
444C3×D4—21no—
445C3×D4—21no—
446C3×D4—22no—
447C3×D4—41no—
448C3×D4D3×Q812yes—
449C3×D4D3×Q812yes—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—31no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—31no—
459C2×C3×C4—41no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—81no—
465C2×C3×C4—81no—
466C2×C3×C4—82no—
467C2×C3×C4—122no—
468C2×C3×C4—241no—
469C2×C3×C4D3×D411yescharacteristic
470C2×C3×C4D3×D411yescharacteristic
471C2×C3×C4C2×#6711yescharacteristic
472C2×C3×C4C2×#6711yescharacteristic
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C23×D311yescharacteristic
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—42no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—81no—
485C2×Dic3—121no—
486C2×Dic3—121no—
487C2×Dic3C2×#6711yescharacteristic
488C2×Dic3C2×#6711yescharacteristic
489C2×Dic3C2×#6711yescharacteristic
490C2×Dic3C2×#6711yescharacteristic
491Dic6—22no—
492Dic6—32no—
493Dic6—32no—
494Dic6—62no—
495Dic6—61no—
496Dic6—61no—
497Dic6—81no—
498Dic6—81no—
499Dic6—121no—
500Dic6—241no—
501Dic6—241no—
502Dic6—241no—
503Dic6—241no—
504C3×C8—61no—
505C3×C8—61no—
506C3⋊C8—21no—
507C3⋊C8—21no—
508C3⋊C8—32no—
509C3⋊C8—32no—
510C3⋊C8—62no—
511C3⋊C8—61no—
512C3⋊C8—61no—
513C3⋊C8—121no—
514C2×C32—42no—
515C2×C32D4×Q811yescharacteristic
516C2×C32C2×#13711yescharacteristic
517C2×C32#57611yescharacteristic
518C2×Q8—31no—
519C2×Q8—61no—
520C2×Q8—61no—
521C2×Q8—91no—
522C2×Q8—181no—
523C2×Q8—181no—
524C2×D4C2×D3211yescharacteristic
525C22×C4—21no—
526C22×C4—61no—
527C22×C4—61no—
528SD16—94no—
529C2×C8—31no—
530C2×C8—31no—
531C2×C8—91no—
532C2×C8—91no—
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—31no—
537C4⋊C4—31no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—91no—
547C4⋊C4—181no—
548C4⋊C4—181no—
549C4⋊C4—181no—
550C4⋊C4—181no—
551C4⋊C4—181no—
552C4⋊C4C2×D3211yescharacteristic
553C22⋊C4—21no—
554C22⋊C4—61no—
555C22⋊C4—61no—
556C42—31no—
557C42—31no—
558C42—181no—
559C42—181no—
560C42—181no—
561C42C2×D3211yescharacteristic
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—21no—
565C22×C3—42no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—81no—
571C22×C3—81no—
572C22×C3C2×D3×D411yescharacteristic
573C22×C3C22×#6711yescharacteristic
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—32no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4—41no—
584C3×C4—41no—
585C3×C4—61no—
586C3×C4—61no—
587C3×C4—61no—
588C3×C4—81no—
589C3×C4—121no—
590C3×C4—121no—
591C3×C4—121no—
592C3×C4—121no—
593C3×C4C2×D3×Q811yescharacteristic
594C3×C4C2×D3×Q811yescharacteristic
595C3×C4#100711yescharacteristic
596C3×C4#101011yescharacteristic
597Dic3—21no—
598Dic3—21no—
599Dic3—21no—
600Dic3—41no—
601Dic3—41no—
602Dic3—41no—
603Dic3—41no—
604Dic3—62no—
605Dic3—62no—
606Dic3—122no—
607Dic3—121no—
608Dic3—121no—
609Dic3—241no—
610Dic3#95112yes—
611C32#338511yescharacteristic, complemented, Sylow
612C23—21no—
613Q8—62no—
614Q8—92no—
615Q8—181no—
616Q8—241no—
617Q8—241no—
618Q8—721no—
619Q8—721no—
620D4—21no—
621D4#379712yes—
622C2×C4—21no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—81no—
632C2×C4—122no—
633C2×C4—181no—
634C2×C4—181no—
635C2×C4—241no—
636C2×C4D3×#6711yescharacteristic
637C2×C4D3×#6711yescharacteristic
638C2×C4C22×D3211yescharacteristic
639C8—61no—
640C8—61no—
641C8—92no—
642C8—181no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—42no—
647C2×C3—42no—
648C2×C3—82no—
649C2×C3#563211yescharacteristic
650C2×C3#575711yescharacteristic
651C2×C3D3×#13711yescharacteristic
652C2×C3Q8×#6711yescharacteristic
653C2×C3C2×#95111yescharacteristic
654C2×C3#583511yescharacteristic
655C22—22no—
656C22—41no—
657C22—41no—
658C22C2×D3×#6711yescharacteristic
659C4—21no—
660C4—21no—
661C4—32no—
662C4—41no—
663C4—61no—
664C4—61no—
665C4—61no—
666C4—121no—
667C4—121no—
668C4—121no—
669C4—121no—
670C4—182no—
671C4—361no—
672C4#6429711yescharacteristic
673C4C2×#379711yescharacteristic
674C3—21no—
675C3#8096011yescharacteristic, complemented
676C3#8363111yescharacteristic, complemented
677C2—42no—
678C2#1059480311yescharacteristic
679C2#1059509611yescharacteristic
680C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC4×D4D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10593856C2semidirect
9. #10590492C2semidirect
10. #10590488C2semidirect
11. #10590418C2semidirect
12. #10590411C2semidirect
13. #10590315C2semidirect
14. #10590292C2semidirect
15. #10590252C2semidirect
105. #3754Q8semidirect
611. C32#3385semidirect
675. C3#80960semidirect
676. C3#83631semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#55392
#105938562
#105927172
C3×#50072
#105914102
#105914082
#105914052
#105914012
#105904922
#105904882
#105904182
#105904112
#105903152
#105902922
#105902522
#836313
#809603